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Shorter Notes: Flat or Open Implies Going Down

David E. Dobbs and Ira J. Papick
Proceedings of the American Mathematical Society
Vol. 65, No. 2 (Aug., 1977), pp. 370-371
DOI: 10.2307/2041925
Stable URL: http://www.jstor.org/stable/2041925
Page Count: 2
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Abstract

Let $R, T$ be commutative rings with identity, and $f: R \rightarrow T$ a unital ring homomorphism. We give an elementary, unified proof of the fact that $f$ has the going down property, if $T$ is flat as an $R$-module or if the induced map $F: \operatorname{Spec}(T)\rightarrow\operatorname{Spec}(R)$ is open.

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